Paper Citation Record · LEDGER

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity

As of 19 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2504.14673.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2504.14673 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:53:31.820282Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

38 of 38 outbound references displayed

verified exact1
verified fuzzy33
unresolved4
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a87beb6f-e66a-4dc1-8f73-aded4e25db79 · outbound

This paper cites Gromov- W asserstein A lignment of W ord E mbedding S paces.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Gromov- W asserstein A lignment of W ord E mbedding S paces

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.358833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e05215ce-ddc0-4bbb-999b-1e63f8eb5cbc · outbound

This paper cites Learning G enerative M odels across I ncomparable S paces.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Learning G enerative M odels across I ncomparable S paces

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.273531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5707913f-1dc9-400c-afdc-f3b764f48900 · outbound

This paper cites Linear A nalysis.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Linear A nalysis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.256389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5938860f-90a2-4fbb-8a37-e31cb6046b1d · outbound

This paper cites Parrilo, and Rekha R.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Parrilo, and Rekha R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.239649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 238c58b2-3a31-4ee8-af56-67013950bce7 · outbound

This paper cites Semidefinite R elaxations of the G romov- W asserstein D istance.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Semidefinite R elaxations of the G romov- W asserstein D istance

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.140867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ff07920d-25b8-4e60-86fb-dcd9439d61bf · outbound

This paper cites Sinkhorn D istances: L ightspeed C omputation of O ptimal T ransport.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Sinkhorn D istances: L ightspeed C omputation of O ptimal T ransport

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.090369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 25c43d98-7f61-4923-8647-9c92c64cfee0 · outbound

This paper cites Gromov- W asserstein O ptimal T ransport to A lign S ingle-cell M ulti-omics D ata.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Gromov- W asserstein O ptimal T ransport to A lign S ingle-cell M ulti-omics D ata

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.074828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 84458f23-0161-41bf-b072-6055f7aea0cd · outbound

This paper cites Optimal T ransport M ethods in E conomics.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Optimal T ransport M ethods in E conomics

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:33.030588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9815011f-5958-46a7-9897-742ab4ef6c9b · outbound

This paper cites Unsupervised A lignment of E mbeddings with W asserstein P rocrustes.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Unsupervised A lignment of E mbeddings with W asserstein P rocrustes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.929325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 40365e07-7a0f-4327-a6be-337d85f61c19 · outbound

This paper cites The NP -hardness of the G romov- W asserstein D istance.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity The NP -hardness of the G romov- W asserstein D istance

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T11:53:31.375522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf3ad0d2-f2ef-41db-94a2-c63fcb818fc3 · outbound

This paper cites From W ord E mbeddings to D ocument D istances.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity From W ord E mbeddings to D ocument D istances

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.914466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8fc17e68-2418-4fcc-b396-94eb3ecce452 · outbound

This paper cites Lasserre.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Lasserre

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.899009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7e16918c-1ad3-4474-8d12-dab9f5736919 · outbound

This paper cites Lasserre.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Lasserre

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.883928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 63171b54-178c-4ad7-9a47-94faac2f3897 · outbound

This paper cites Lasserre.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Lasserre

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.759877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2ac495b2-5205-467f-ae23-0b3d1e5aa2b0 · outbound

This paper cites On the use of G romov- H ausdorff D istances for S hape C omparison.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity On the use of G romov- H ausdorff D istances for S hape C omparison

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.655480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 78d30340-ed9c-4b1a-aef0-ea47361e21f0 · outbound

This paper cites Gromov-- W asserstein D istances and the M etric A pproach to O bject M atching.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Gromov-- W asserstein D istances and the M etric A pproach to O bject M atching

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.640999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 991d8692-12bf-4bd9-8cb4-be3ea0d8f450 · outbound

This paper cites Sharp A symptotic and F inite-sample R ates of C onvergence of E mpirical M easures in W asserstein D istance.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Sharp A symptotic and F inite-sample R ates of C onvergence of E mpirical M easures in W asserstein D istance

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.626955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation df39fada-612d-49d3-b151-4083cceac219 · outbound

This paper cites an unresolved cited work.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:53:32.611365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c17c89da-1f64-4dc9-929e-ee893773dbbe · outbound

This paper cites Computational O ptimal T ransport: W ith A pplications to D ata S cience.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Computational O ptimal T ransport: W ith A pplications to D ata S cience

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.596069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 83a18045-0421-4ab0-b725-11450d652909 · outbound

This paper cites Gromov- W asserstein A veraging of K ernel and D istance M atrices.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Gromov- W asserstein A veraging of K ernel and D istance M atrices

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.581445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 264595f6-ffee-4e3a-b1b5-78591aaa620b · outbound

This paper cites On the Wasserstein alignment problem.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity On the Wasserstein alignment problem

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T11:53:31.538438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d946c43b-6ad4-4a9d-9511-2752dbef28a5 · outbound

This paper cites A Mathematical View of Interior-Point Methods in Convex Optimization.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity A Mathematical View of Interior-Point Methods in Convex Optimization

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.567691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e1355f84-ada3-4475-808a-d66949a65176 · outbound

This paper cites Entropic G romov- W asserstein D istances: S tability and A lgorithms.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Entropic G romov- W asserstein D istances: S tability and A lgorithms

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.552936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a45aa8cf-19ce-4aa1-a935-cdb2f80177d0 · outbound

This paper cites The M oment P roblem on C ompact S emi-algebraic S ets.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity The M oment P roblem on C ompact S emi-algebraic S ets

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.529378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e484c23a-4737-4164-894f-c98cead9da32 · outbound

This paper cites P-complete A pproximation P roblems.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity P-complete A pproximation P roblems

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.439103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 457a8446-a42e-47cc-9fb5-067af0f6ed9b · outbound

This paper cites Linear- T ime G romov W asserstein D istances using L ow R ank C ouplings and C osts.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Linear- T ime G romov W asserstein D istances using L ow R ank C ouplings and C osts

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.392251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 87ba2a77-6bb4-4a3e-ad93-b906c4b7562c · outbound

This paper cites Entropic M etric A lignment for C orrespondence P roblems.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Entropic M etric A lignment for C orrespondence P roblems

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.376112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c31c055a-31d3-431e-8806-b631ff9023e0 · outbound

This paper cites On the G eometry of M etric M easure S paces.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity On the G eometry of M etric M easure S paces

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.361010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b448bfa4-b863-49e7-af9e-b3cd4cd48a2b · outbound

This paper cites The S pace of S paces: C urvature B ounds and G radient F lows on the S pace of M etric M easure S paces , volume 290.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity The S pace of S paces: C urvature B ounds and G radient F lows on the S pace of M etric M easure S paces , volume 290

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.344188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6703b4c0-c01a-42b2-ad20-a581b3dd36a9 · outbound

This paper cites Sum-of- S quares H ierarchy for the G romov W asserstein P roblem.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Sum-of- S quares H ierarchy for the G romov W asserstein P roblem

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.315550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eb0f02ce-c04b-4018-ae0a-4a64920215cc · outbound

This paper cites Optimal T ransport for T ransfer L earning across S paces.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Optimal T ransport for T ransfer L earning across S paces

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.256288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9d31435b-954f-4a82-ac92-df1cfc0b906c · outbound

This paper cites Aligning I ndividual B rains with F used U nbalanced G romov W asserstein.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Aligning I ndividual B rains with F used U nbalanced G romov W asserstein

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.239022Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation af56a33a-8020-4ab1-87d7-43d3747d9a29 · outbound

This paper cites A contribution to Optimal Transport on incomparable spaces.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity A contribution to Optimal Transport on incomparable spaces

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-16T11:53:31.793560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b1146c8-a5ef-4acf-964b-9e1062e471af · outbound

This paper cites Fused G romov- W asserstein D istance for S tructured O bjects.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Fused G romov- W asserstein D istance for S tructured O bjects

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.223226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e13d9b7c-fe24-45e4-a39a-49d8e8c89e8f · outbound

This paper cites Online Graph Dictionary Learning.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Online Graph Dictionary Learning

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:53:31.895274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b73f763b-22cc-4f08-b59d-3291140da8c0 · outbound

This paper cites Optimal T ransport: O ld and N ew.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Optimal T ransport: O ld and N ew

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.204900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1abc962f-6303-4394-90a8-dd75fd2ecf4f · outbound

This paper cites Gromov- W asserstein L earning for G raph M atching and N ode E mbedding.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Gromov- W asserstein L earning for G raph M atching and N ode E mbedding

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.187547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 60a79517-ad83-4c62-8b82-4bb7bda2ca4c · outbound

This paper cites Sriperumbudur.

Moment Sum-of-Squares Hierarchy for Gromov Wasserstein: Continuous Extensions and Sample Complexity Sriperumbudur

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:53:32.120532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.